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Jamia Millia Islamia Previous Year Questions (PYQs)

Jamia Millia Islamia Probability Critical Thinking PYQ

Jamia Millia Islamia PYQ
Find the remainder when $67^{99}$ is divided by 7.





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2018 PYQ

Solution

$67 \equiv 4 \pmod7$, so $4^3 \equiv 1$. $99$ is multiple of 3 → remainder $=1$.
Jamia Millia Islamia PYQ
Three letters are dictated to three persons and an envelope is addressed to each of them. The letters are inserted into the envelopes at random so that each envelope contains exactly one letter. What is the probability that at least one letter is in its proper envelope?





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2019 PYQ

Solution

Total permutations of 3 letters = $3! = 6$. Derangements (no letter in correct envelope) = $!3 = 2$. Hence, number of favorable cases (at least one correct) = $6 - 2 = 4$. Probability $= \dfrac{4}{6} = \dfrac{2}{3}$.
Jamia Millia Islamia PYQ
A tourist visits four cities A, B, C and D in a random order. What is the probability that he visits A before B?





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2019 PYQ

Solution

Out of all $4! = 24$ permutations, in half of them A comes before B, and in the other half B comes before A. Therefore probability = $\dfrac{1}{2}$.

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